Problem: Simplify the following expression: $ x = \dfrac{1}{8} - \dfrac{2}{-2t + 4} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-2t + 4}{-2t + 4}$ $ \dfrac{1}{8} \times \dfrac{-2t + 4}{-2t + 4} = \dfrac{-2t + 4}{-16t + 32} $ Multiply the second expression by $\dfrac{8}{8}$ $ \dfrac{2}{-2t + 4} \times \dfrac{8}{8} = \dfrac{16}{-16t + 32} $ Therefore $ x = \dfrac{-2t + 4}{-16t + 32} - \dfrac{16}{-16t + 32} $ Now the expressions have the same denominator we can simply subtract the numerators: $x = \dfrac{-2t + 4 - 16 }{-16t + 32} $ Distribute the negative sign: $x = \dfrac{-2t + 4 - 16}{-16t + 32}$ $x = \dfrac{-2t - 12}{-16t + 32}$ Simplify the expression by dividing the numerator and denominator by -2: $x = \dfrac{t + 6}{8t - 16}$